Harry and friends had to go out and destroy every single horcrux completely, so the basilisk injuring him didn't get rid of the horcrux. When Harry gets killed (but it's Harry so he survived) THATS when the horcrux is destroyed.
Basically, the Basilisk didn't kill Harry but when he dies the horcrux is destroyed. Harry comes back but the horcrux doesn't.
-Fueled by the game-changing use of steam power, the Industrial Revolution began in Britain and spread to the rest of the world, including the United States, by the 1830s and '40s.
